A rectangular solid black has length 10cm, breadth 5cm and height 2cm. If it lies on a horizontal surface, and has density 100kg/m3 3 , calculate the pressu...
A rectangular solid black has length 10cm, breadth 5cm and height 2cm. If it lies on a horizontal surface, and has density 100kg/m3, calculate the pressure it exerts on the surface.
Answer Details
To calculate the pressure that the rectangular solid exerts on the surface, we need to use the formula for pressure:
Pressure = Force / Area
In this case, the force is the weight of the rectangular solid, which we can calculate using the formula:
Weight = Mass x Gravity
The mass of the rectangular solid can be calculated using its density and volume:
Mass = Density x Volume
The volume of the rectangular solid is simply its length x breadth x height:
Volume = Length x Breadth x Height = 10 cm x 5 cm x 2 cm = 100 cm3
We need to convert this volume to cubic meters to use the density given in kg/m3:
Volume = 100 cm3 = 0.0001 m3
Now we can calculate the mass:
Mass = Density x Volume = 100 kg/m3 x 0.0001 m3 = 0.01 kg
The gravity is the acceleration due to gravity, which we can assume to be 9.81 m/s2. Therefore, the weight is:
Weight = Mass x Gravity = 0.01 kg x 9.81 m/s2 = 0.0981 N
Now we can use this weight to calculate the pressure on the surface. The surface area in contact with the rectangular solid is simply its length x breadth:
Area = Length x Breadth = 10 cm x 5 cm = 50 cm2
We need to convert this area to square meters:
Area = 50 cm2 = 0.005 m2
Therefore, the pressure is:
Pressure = Force / Area = 0.0981 N / 0.005 m2 = 19.62 N/m2
We can convert this to units of N/cm2 or N/mm2 if desired. This is equivalent to:
Pressure = 0.1962 N/cm2 = 0.0001962 N/mm2
So the pressure that the rectangular solid exerts on the surface is 19.62 N/m2, which is approximately 20 N/m2. Therefore, the answer is 200 N/m2.